On uniqueness for the generalized choquard equation

Vladimir Georgiev, George Venkov

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We consider the generalized Choquard equation describing trapped electron gas in three dimensional case. The study of orbital stability of the energy minimizers (known as ground states) depends essentially in the local uniqueness of these minimizers. The uniqueness of the minimizers for the case p = 2, i.e. for the case of Hartree–Choquard is well known. The main difficulty for the case p ≠ 2 is connected with possible lack of control on the Lp norm of the minimizers. Our main result treats the local uniqueness of radial positive minimizers for p ∈ (5∕3, 7∕3).

Original languageEnglish
Title of host publicationTrends in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Pages263-278
Number of pages16
DOIs
Publication statusPublished - 2020

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Keywords

  • Choquard equation
  • Ground states
  • Local uniqueness

ASJC Scopus subject areas

  • Mathematics(all)

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